Algebra 2 Traditional

RFA ) Solve the following absolute value equality: 2+|x-8| = 3x-6 2) Solve the following inequalities and graph the solution sets ◦ 9(2x+3)>10 ◦ 7-2m ≥ 0

Representing the solutions of equalities You can think of the solution(s) to a given equation as solution sets. Equation Set notation Interval notation 3x+1 = 10 2x + 1 = 2x + 1 3x+4 = 3x – 7

Representing the solutions of equalities You can think of the solution(s) to a given equation as solution sets. Equation Set notation Interval notation 3x+1 = 10 {3} [3] 2x + 1 = 2x + 1 {x| x is a real number} 3x+4 = 3x – 7 { } ( )

Representing the solutions of in-equalities -2x + 4 > 8 -2x > 4 X < -2 {x| x<-2} (set builder notation) (-∞, -2) (interval notation) Number line (Draw below)

Quick final note… If an inequality includes an “or equal to” part, that part remains even if you need to flip the inequality.

Before the next section: Operations with Sets Goals: ◦ Know what it means to find the “intersection” and “union” between multiple sets. ◦ Be able to graph unions and intersections on number lines ◦ Define what an empty set, or “null” set is

Union & Intersections Union: the set of elements in one set, another, or both means the union of sets “A” and “B” Intersection: The set of elements that are in two sets at the same time means the intersection of sets “F” and “G”

Pictorial Representations

Null or Empty Sets Sets with no elements in them are called null or empty sets. { } OR

Union and Intersection on the number line Union x 0 Intersection x 0

Absolute Value Inequalities Everything you EVER wanted to know about |2x-3|=, 9!

Type of Absolute Value Problem |ax+b| What it means in terms of distance What kind of solution you are going to get |ax+b|=k A specific distance “k” (to the left or right) away from zero on number line |ax+b|>k Two inequalities that won’t overlap (so link them with a “U”) |ax+b|<k ax+b is BETWEEN “k” distance from zero to the left and “k” distance to the right

Type of Absolute Value Problem |ax+b| What it means in terms of distance What kind of solution you are going to get |ax+b|=k A specific distance “k” (to the left or right) away from zero on number line Two specific solutions (assuming k>0) |ax+b|>k ax+b must be AT LEAST “k” distance away from zero on number line Two inequalities that won’t overlap (so link them with a “U”) |ax+b|<k ax+b is BETWEEN “k” distance from zero to the left and “k” distance to the right Two inequalities that intersect, so find the intersection interval

Group Work/HW Group Work: Homework odd Test early next week on chapter 1!